The isomorphism problem for all hyperbolic groups

Details The isomorphism problem for all hyperbolic groups The isomorphism problem for all hyperbolic groups

2010-02-12

arxiv.org/abs/1002.2590v2

Mathematics

Group Theory

71 pages, 4 figures

Scientific paper

We give a solution to Dehn's isomorphism problem for the class of all hyperbolic groups, possibly with torsion. We also prove a relative version for groups with peripheral structures. As a corollary, we give a uniform solution to Whitehead's problem asking whether two tuples of elements of a hyperbolic group $G$ are in the same orbit under the action of $\Aut(G)$. We also get an algorithm computing a generating set of the group of automorphisms of a hyperbolic group preserving a peripheral structure.

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